<p>Distributional regression (DR) refers to regression methods that model the entire conditional probability distribution of a response variable given a set of explanatory variables. The generalized additive model for location, scale and shape (GAMLSS) is a common framework of DR, extending traditional regression models (such as linear models, generalized linear models and generalized additive models) by modelling the mean, variance, skewness and tail behaviour as functions of explanatory variables. The influence of explanatory variables on variability, quantiles and exceedance probabilities can thus be directly measured, providing deeper insight into underlying data-generating process. DR is ideal for applications in which predicting uncertainty and extreme events — and hence risk assessment — is critical. In this Primer, we provide an overview of GAMLSS-based DR, including the theoretical background and guidelines for practical implementation and model checking. Case studies across disciplines demonstrate that GAMLSS captures intrinsic distributional features often missed by classical mean-based regression and machine learning approaches. Finally, we highlight future directions, particularly in combination with machine learning.</p>